Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C32×C22⋊C4 ⋊ C8 |
| Sylow | C32 ⋊ #1850 |
414 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2^7,3^2|a^2=f,b^2=f,f^2=g,b^a=bd,c^a=ce,h^a=hi^2,i^a=h^2,h^b=h^2i,i^b=h,h^f=h^2i^2,i^f=h^2i,h^g=h^2,i^g=i^266 conjugacy classes — view the full character table.
| maximal subgroup of | #72220446, #72220543, #120×AGL(1,𝔽9), … |
| maximal normal subgroup of | #72220446, #72220543, #120×AGL(1,𝔽9), … |
| maximal quotient of | #72252970 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 20386);